This is meant to provide some background for my next post on the Tea Party since I know that some people don't terribly like the term populism. Personally, I think it is a useful term but does tend to fall into the trap of either being an "I know it when I see it" undefined term or to be shorthand for "I think that's a stupid idea."
However, I think there is a common theme running through political ideas referred to as populist, whether talking about modern times, the 18th century, or Athens and Rome, so will be trying to give my explanation of what this common theme is. A brief warning, this is a topic that interests me but I have done no dedicated research on so this is necessarily incomplete and only half thought out. Read it with that in mind.
Basically, I think the distinctive feature of populism separating it from other forms of political thought is that it concerns itself primarily with advocating for a change in social relations as opposed to advocating for policies that deal with technical aspects of living together in society or with the specific distribution of power or wealth (though these things are likely also impacted by populist policies, they are simply not these policies' distinctive feature). This is why populist policies often seem so absurd to those who don't share these goals, the specific policies are ultimately more symbolic than they are concrete paths to a narrowly defined policy objective.
This trend displays itself in many of the major political movements that have been called populist. For instance, in the Roman Republic the populist label often refers to policies aimed towards restoring the balance of the citizen-soldier-farmer that those advocating for these policies felt was threatened. They wanted to solidify a social relationship that was seen as under threat (of course some distinction has to be drawn between the populism of the Marius and the party of Caesar, though the distinction is clear enough if you're thinking of what later writers continued to call populist without specific reference to party labels of the day). Other populisms follow this pattern. 19th century American populism wanted to preserve rural agriculture against corporate (mostly manufacturing) interests and populist movements in Europe often imagined a new social order through communism.
What's distinctive is that populism imagines that basic social relationships can be heavily influenced through government policy. This differs from other forms of political thought that tend to see government's power in a more narrow sense. Of course, populism can imagine government's role in social relations as either a force for good or ill, but either way populism sees government as playing a key role in basic social relations. I will admit to having very little personal sympathy for populism of any type, I see government as having to react to existing social relationships and change being exerted on them by forces largely outside government's control. While government is not entirely helpless in this aspect, its powers are very limited.
My apologies for using some vague terminology in this post, as I stated at the beginning these ideas are still under researched and half-backed. I felt it was a necessary intro to give at least a loose definition for my next post on the Tea Party so went ahead with it.